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The value of sum(r=1)^n(-1)^(r+1)(^^n C ...

The value of `sum_(r=1)^n(-1)^(r+1)(^^n C r)/(r+1)` is equal to `-1/(n+1)` b. `1/n` c. `1/(n+1)` d. `n/(n+1)`

A

`-1/(n+1)`

B

`-(1)/(n)`

C

`(1)/(n+1)`

D

`(n)/(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(r=1)overset(n)sum(-1)^(r+1)(.^(n)C_(r))/((r+1))= (1)/(n+1)underset(r=1)overset(n)sum(-1)^(r+1).^(n+1)C_(r+1)`
`= 1/(n+1)(0-1+(n+1))= (n)/(n+1)`
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